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The use of two types of phase modulations arising from the coherent rotations of ortho-hydrogen and para-hydrogen to generate an intense ultrashort ultraviolet pulse without substantial generation of sub-pulses was demonstrated. This technique allows use of a high-energy long-probe pulse in the pump-probe regime for generating a high-energy compressed pulse. A 100-fs ultraviolet pulse was compressed to 11-fs by the phase modulation followed by dispersion compensation with chirped mirrors.
©2008 Optical Society of America
1. Introduction
Because an ultrashort ultraviolet (UV) pulse allows study of an ultra-fast phenomenon in an organic molecule, several techniques have been reported to generate such an optical pulse [1–4]. For instance, a Raman-based technique [3,5–10], in which a coherent molecular motion induced by an intense pump pulse is used to modulate the frequency of a probe pulse (UV pulse), allows generation of a single sub-4 femtosecond (fs) UV pulse [8]. The technique is suitable for generation of an extremely short UV pulse, but the energy of the ultrashort pulse is limited at a low value. This is because the energy of the probe pulse must be sufficiently low to prevent ionization of Raman-active molecules, because ionization leads to induction of undesired phenomena (e.g., deterioration of beam profile). A short 15-fs probe pulse used in such studies has high peak intensity and readily ionizes the molecules, so the energy of the pulse must be low. This problem is solved by a long probe pulse whose peak intensity is low. The low intensity leads to a high energy threshold for ionization, allowing use of a high-energy probe pulse for generation of a high-energy ultrashort UV pulse. This leads to another problem: generation of sub-pulses in the compressed temporal profile [10]. The sub-pulses in the temporal profile confine the application range of the generated pulse to a narrow range, and must be removed from the temporal profile.
In this report, to reduce the intensity of the sub-pulses, a method based on two phase-modulation processes arising from two types of coherent motions was investigated. Interference between the two phase-modulation processes led to suppression of the periodicity in the phase-modulation process. By controlling the time delay of a probe pulse with respect to a pump pulse, the intensity of the sub-pulses in the temporal profile was substantially decreased in comparison with the case where only a coherent motion was induced to modulate the phase of a probe pulse [10] and the case where the time delay was not controlled [11].
2. Theoretical description
The phase-modulation process of a probe pulse in this study is similar to that reported elsewhere [3,5]. A coherent molecular motion is induced through transient stimulated Raman scattering [10] rather than impulsive stimulated Raman scattering [3,5–9]; and two types of coherent molecular motions are considered in this study. A linearly polarized probe pulse described as follows is considered:
where A(z,t), z, and k 0 are the slowly varying envelope, propagation distance, and propagation coefficient of the probe pulse, respectively. The coherent rotation of ortho-hydrogen (o-H2) and that of para-hydrogen (p-H2) are considered in the following description, but similar discussion is applicable to other molecular species and motions. When the coherent rotations of o-H2 and p-H2 are induced simultaneously in H2 gas by an intense pump pulse, the probe pulse propagating through the coherent rotations is modulated by induced polarization whose slowly varying amplitude is expressed as:
where N i, (∂α/∂Q)i, Q i(z, t)=Q i(t-z/ν pump), ν pump are the molecular density, the SRS coupling constant, the amplitude of a coherent motion, and the group velocity of the pump pulse, respectively. When the time delay of the probe pulse with respect to the pump pulse is much smaller than the decay times of the amplitudes of the coherent molecular motions, the decays can be neglected. The amplitudes can therefore be expressed using constant values, Q o0 and Q p0 [5]:
where Ωo and Ωp are the angular frequencies of the coherent rotations, ϕo and ϕp show the relative phases of the rotations, and Δt is the time delay of the probe pulse with respect to the pump pulse. Equation (3) is satisfied for positive values of Δt. If the group velocity mismatch between the pump and probe pulses, and the group-velocity dispersion in the Raman medium are neglected, the interaction between the probe pulse and the polarization p Ram is described as [12]:
where n 0 is the refractive index of the Raman medium at the wavelength of the probe pulse, and c is the speed of light in vacuum. A coordinate system (z’, τ) moving at the group velocity of the probe pulse is considered here. After the phase modulation during the propagation distance z’, the phase of the probe pulse is modulated to:
Equation (5) is used to simulate how the phase of a transform-limited 100-fs Gaussian pulse is modulated by the coherent rotations of o-H2 and p-H2. If only the coherent rotation of o-H2 is induced, the phase of the probe pulse is modulated sinusoidally with the period of 57 fs (Fig. 1(a)) and the periodical (sinusoidal) structure is caused within the temporal profile.
Fig. 1. (a) Phase change ϕ(z’, τ)-ϕ(0, τ) calculated under the assumption that ϕ o=ϕ p=0 rad and β oz’=β pz’=1 rad. The solid curve and dotted curve are calculated assuming the case where the two types of coherent rotations are induced, and the case where only the coherent rotation of ortho-H2 is induced, respectively. (b) Expanded view of (a).
After compensation for group-delay dispersion (GDD) induced by the phase modulation process, periodical phase-locking points appear in the temporal profile of the probe pulse, resulting in generation of a pulse train consisting of a main pulse and several sub-pulses separated by 57 fs (shaded curve in Fig. 2(a)) [10]. If the coherent rotation of p-H2 whose rotational period is 94 fs is simultaneously induced in addition to that of o-H2, the curve of the phase change varies to the complicated structure shown by a solid line in Fig. 1(a). Because the multiplication of 57 fs by 5 is nearly equal to the multiplication of 94 fs by 3, a part of the structure is repeated with a period of ca. 284 fs. Because the pulse width of the probe pulse (100 fs) is shorter than the period (284 fs), periodical phase-locking points with the period of 284 fs do not appear in the compressed temporal profile. Instead, by changing the time delay Δt of the probe pulse continuously, the same spectrum of the modulated probe pulse is observed with the period of 284 fs, which allows confirmation of whether the two types of coherent rotations are simultaneously induced.
The intensity of the sub-pulses in the compressed temporal profile in the case of the induction of the two types of coherent rotations is smaller than that in the case of the induction of only the coherent rotation of o-H2, provided that the time delay of the probe pulse is adjusted appropriately. The temporal profiles of the compressed pulses after the dispersion compensation are calculated in Fig. 2(a) using Eq. (5) under the assumption of time delays Δt of 16.6 fs and 72 fs. The intensity of the sub-pulses in the case of the induction of the two types of coherent rotations and the time delay of 16.6 fs is smaller than those in the case that only the coherent rotation of o-H2 is induced. In the case of the time delay of 72 fs, the intensity of the sub-pulses is enhanced rather than reduced.
Fig. 2. (a) Calculated temporal profiles and (b) spectra of ultrashort pulses compressed by compensation for group-delay dispersion. In both figures, the waveforms are calculated assuming the time delays of 16.6 fs (solid line) and 72 fs (broken line). The frequency of a 100-fs probe pulse is modulated by the phase modulations arising from the coherent rotations of o-H2 and p-H2. In the shaded curves, the frequency is modulated by the phase modulation by only the coherent rotation of o-H2, and the time delay is 16.6 fs. The waveforms at the time delay of 72 fs are almost identical to those at 16.6 fs. Each waveform is normalized with respect to its peak intensity.
The condition of the low-intensity sub-pulses can be realized by simultaneous observation of the spectrum of the modulated probe pulse and adjustment of the time delay of the probe pulse because the spectra in the two cases of the time delays are different from each other. Spectra corresponding to the temporal profiles shown in Fig. 2(a) are calculated in Fig. 2(b) by Fourier transform. The feature of each spectrum depends on the time delay Δt. The spectral structure between some peaks (e.g., between the two peaks at 11 THz and 18 THz) is smooth in the case of the time delay of 16.6 fs (solid line in Fig. 2(b)), whereas the spectral peaks are discretely distributed in the case of the time delay of 72 fs (broken line in Fig. 2(b)). Reduction of the intensity of the sub-pulses is achieved for a probe pulse sufficiently short compared with the period of 284 fs. For a long probe pulse, for instance, a 200-fs probe pulse [6], the phase of the probe pulse after phase modulation is complicated (see Fig. 1(a)) and hence reduction of the intensity of the sub-pulses by control of the time delay of the probe pulse is difficult.
3. Experimental
A fs UV pulse (393 nm) was produced by doubling the frequency of a near-infrared (NIR) fs pulse (784 nm) emerging from a Ti-sapphire chirped pulse amplifier (1.5 mJ, 100 fs, 1 kHz, Concerto, Thales Laser) using a LiB3O5 frequency-doubling crystal (1.58-mm thick, cutting angles of θ=90°, ϕ=33.2°, CASTECH). The UV pulse and NIR pulse are hereafter denoted by probe pulse and pump pulse, respectively. The former was separated spatially from the pump pulse to control the time delay of the probe pulse using an optical delay line. The two pulses were spatially overlapped again and focused into a Raman cell filled with normal H2 gas (10 atm) using an aluminium-coated concave mirror (f=500 mm). The energies of the input pump and probe pulses were 270 µJ and 28 µJ, respectively. The output probe beam from the cell was collimated with a concave mirror (f=500 mm) before measurement of the spectrum with a fiber-coupled, multi-channel spectrometer (Avaspec-2048, wavelength resolution of 0.4 nm, Avantes) whose wavelength dependence of the sensitivity of the spectrometer was calibrated with a standard lamp. A self-diffraction frequency-resolved optical gating (SD-FROG) system [13] consisting of a SD autocorrelator and the multi-channel spectrometer was also used for characterization of the temporal profile of the pulse. The autocorrelator included two metal-coated beam splitters with a thickness of 1.5 mm, a concave mirror (f=200 mm) and a 100-µm-thick sapphire plate.
4. Results and discussion
The spectral width of the probe pulse (393 nm, a FWHM of 1.8 nm) was extended to a width more than ten-times broader (20 nm) than the width of the input probe pulse. The frequency of the probe pulse was also modulated by self-phase modulation (SPM), but its effect was small and the spectral width was mainly determined by the efficiency in the induction of the coherent rotations. The structure of the spectrum was denser than that of the pulse modulated by only the coherent rotation of o-H2 [10], and depended on the time delay of the input probe pulse with respect to the pump pulse. The intensity of the fundamental emission (393 nm) varied periodically with a period of 284 fs (Fig. 3(a)), suggesting that the probe pulse was modulated by the coherent rotations of o-H2 and p-H2. When the time delay was adjusted at a delay providing low conversion efficiency (y in Fig. 3(a)), the spectrum consisted of numerous small peaks (in Fig. 3(b)). In the case of the time delay, providing high conversion efficiency (x in Fig. 3(a)), the spectral structure was smooth (x in Fig. 3(b)). The former and latter cases qualitatively correspond to the cases of the time delay of 72 fs and 16.6 fs in the numerical calculations, respectively (Fig. 2(b)). In this experiment, the time delay was adjusted to the latter case to generate an ultrashort pulse without generation of intense sub-pulses (x in Fig. 3(b)).
Fig. 3. (a) Variation of peak intensity of the fundamental emission (393 nm) as a function of the time delay of the probe pulse (probe delay) with respect to the pump pulse. The intensity was divided by the peak intensity of the fundamental emission measured in the case where the coherent rotations were not induced. (b) Spectra of probe pulses emitted from the Raman cell. The probe delays were adjusted to 2270 fs (x in Fig. 1, solid line) and 2670 fs (y in Fig. 1, broken line), respectively. The inset shows an expanded view of a spectral structure.
The GDD involved in the output probe pulse was compensated by 31-times reflections of a pair of chirped mirrors producing a negative GDD of –25 fs2 per bounce (100688, Layertec). Many reflections were realized by reducing the beam diameter to 2 mm using an aperture, leading to reduced energy of the probe pulse after the GDD compensation to 5 µJ. It also led to the change of the spectrum from that shown in Fig. 3(b) to that shown in Fig. 4(a). This change occurred because coherent rotations were induced efficiently in the center part of the pump beam. The frequency of the probe pulse was therefore strongly modulated at the center of the probe beam compared with the outside of the beam. The probe pulse was then sent to the SD autocorrelator to measure a SD-FROG trace. The trace confirmed that the GDD in the pulse was successfully compensated for with the mirrors because the trace was distributed orthogonally to the delay axis [13]. The trace was analyzed using a commercial algorithm supplied by FemtoSoft Technologies. The FROG error [14] of 0.0085 in the analysis was sufficiently small, but the spectrum retrieved from the trace was slightly different from the spectrum measured with the multi-channel spectrometer (Fig. 4(a)). This may be due to the small spatial chirp in the pulse, arising from the slight difference in the propagation directions of the pump and probe pulses in the Raman cell [10,15]. We found that when the amount of the spatial chirp was large, the difference in the spectrum for the measured and retrieved ones was also large. The propagation directions of the pump and probe beams were therefore carefully aligned in the experiment. Complete removal of the spatial chirp was difficult.
The retrieved temporal profile consisted of an intense main pulse and small sub-pulses (Fig. 4(b)). The energy ratio between the main pulse and the background component consisting of the sub-pulses was one-half. The intensity of the sub-pulses, which was one-third of the intensity of the main pulse, was lower than that in the temporal profile of the pulse obtained in the case of the phase modulation arising from only the coherent rotation of o-H2 [10]. This suggests that use of the two types of coherent rotations of o-H2 and p-H2 is useful to reduce the intensity of the sub-pulses. The pulse width of the main pulse was 11 fs, about nine-times shorter than that of the probe pulse before phase modulation. The inverse Fourier transforms of the measured and retrieved spectra showed nearly single-pulse structures, with pulse widths of 8 fs (shaded curve in Fig. 4(b)). The probe pulse was therefore not compressed to the Fourier-transform-limited width due to the uncompensated part of high-order dispersion, which is suggested from the complicated curve of the retrieved spectral phase (Fig. 4(b)). The complicated curve may relate to the oscillation structure in the GDD curve of the chirped mirrors, as well as the high-order dispersion induced in transparent materials (e.g., output window of the Raman cell). The complicated phase modulation in the time domain by coherent rotations (Fig. 1) would have been a cause of the structure. To compensate the distortion in the spectral phase completely, a deformable mirror is useful because it allows compensation of high-order phase distortion [16]. This should lead to a pulse width shorter than 11 fs, and complete removal of the sub-pulses in the temporal structure.
Fig. 4. (a) Spectrum of the probe pulse measured at the entrance of the autocorrelator using the multi-channel spectrometer (broken line), and the spectrum retrieved from the measured SD-FROG trace (solid line). The retrieved spectral phase is also shown in the figure (dotted line). Each spectrum in the figure is normalized by its peak intensity. (b) Temporal profile (solid line) and phase (dotted line) of the ultrashort pulse retrieved from the SD-FROG trace. The shaded curve shows the intensity profile calculated by the inverse Fourier transform of the measured spectrum assuming the case of the transform-limited pulse.
5. Conclusion
The two types of coherent rotations of o-H2 and p-H2 are used to modulate the frequency of a 100-fs UV pulse for generating an ultrashort UV pulse without substantial generation of sub-pulses. By compensation for GDD among the spectral components generated by the phase modulation, an 11-fs ultrashort UV pulse was generated without generation of intense sub-pulses. The intensity of the sub-pulses depends on the time delay of the UV pulse with respect to the phases of the coherent rotations, and therefore precise adjustment of the delay is essential in this regime. In future work, the intensity of the sub-pulse will be further reduced by modulating a UV pulse by SPM in addition to phase modulation by coherent molecular motions, and also by use of a deformable mirror.
Acknowledgments
This research was supported by a Grant-in-Aid for the Japan Society for the Promotion of Science (JSPS) Fellows (project number of 06J09678), Grant-in-Aid for Scientific Research, and a Grant-in-Aid for the Global COE program, “Science for Future Molecular Systems,” from the Ministry of Education, Culture, Science, Sports and Technology of Japan.
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